Finite Group Databasebeta

← C43×#12687 #24932704

Subgroups — C43×#12687 #24932704

Order 11008.

2508 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 2508 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C43C211yesmaximal, characteristic
2C2×C43×AΣL(1,𝔽16)C214yesmaximal, complemented
3C43×#1783C211yesmaximal, characteristic, complemented
4C43×#1781C211yesmaximal, characteristic, complemented
5C26×C43C411yescharacteristic, complemented
6C23×D4×C43—21no—
7C23×D4×C43C2211yescharacteristic
8C2×#120×C43—21no—
9C2×#120×C43—21no—
10C2×#120×C43—28no—
11C2×#120×C43C412yescomplemented
12C2×#120×C43C2212yes—
13C22×C22⋊C4×C43—21no—
14C22×C22⋊C4×C43C411yescharacteristic, complemented
15C2×#100×C43—21no—
16C2×#100×C43C2212yescomplemented
17C2×#99×C43—21no—
18C2×#99×C43C2212yescomplemented
19C43×#407—21no—
20C43×#379—21no—
21C43×AΣL(1,𝔽16)—28no—
22C25×C43—21no—
23C25×C43—21no—
24C25×C43—24no—
25C25×C43—48no—
26C25×C43—42no—
27C25×C43—42no—
28C25×C43C2×C411yescharacteristic
29C25×C43C2×C412yes—
30C25×C43D411yescharacteristic
31C22×D4×C43—28no—
32C22×D4×C43—22no—
33C22×D4×C43—22no—
34C22×D4×C43—24no—
35C22×D4×C43—42no—
36C22×D4×C43—42no—
37C22×D4×C43—48no—
38C22×D4×C43C2×C411yescharacteristic
39C22×D4×C43D411yescharacteristic
40C22×D4×C43D411yescharacteristic
41C22×D4×C43C2311yescharacteristic
42C23×C4×C43—21no—
43C23×C4×C43D411yescharacteristic
44C2×M16×C43—22no—
45#120×C43—28no—
46#120×C43—28no—
47#120×C43—24no—
48#120×C43—24no—
49#120×C43—24no—
50#120×C43D418yes—
51C2×C22⋊C4×C43—28no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43—22no—
54C2×C22⋊C4×C43—22no—
55C2×C22⋊C4×C43—24no—
56C2×C22⋊C4×C43—22no—
57C2×C22⋊C4×C43—42no—
58C2×C22⋊C4×C43C2×C412yes—
59#100×C43—24no—
60#100×C43—42no—
61#99×C43—24no—
62#99×C43—42no—
63C22⋊C8×C43—42no—
64C24×C43—24no—
65C24×C43—28no—
66C24×C43—22no—
67C24×C43—22no—
68C24×C43—22no—
69C24×C43—22no—
70C24×C43—24no—
71C24×C43—22no—
72C24×C43—22no—
73C24×C43—22no—
74C24×C43—41no—
75C24×C43—44no—
76C24×C43—42no—
77C24×C43—48no—
78C24×C43—432no—
79C24×C43—416no—
80C24×C43—42no—
81C24×C43—44no—
82C24×C43—48no—
83C24×C43—42no—
84C24×C43—42no—
85C24×C43—44no—
86C24×C43—416no—
87C24×C43—432no—
88C24×C43—48no—
89C24×C43—42no—
90C24×C43—42no—
91C24×C43—48no—
92C24×C43C22⋊C411yescharacteristic
93C24×C43C22⋊C411yescharacteristic
94C24×C43C22⋊C411yescharacteristic
95C24×C43C22⋊C414yescomplemented
96C24×C43C22×C411yescharacteristic
97C24×C43C2×D411yescharacteristic
98C2×D4×C43—28no—
99C2×D4×C43—22no—
100C2×D4×C43—22no—
101C2×D4×C43—22no—
102C2×D4×C43—22no—
103C2×D4×C43—22no—
104C2×D4×C43—28no—
105C2×D4×C43—41no—
106C2×D4×C43—41no—
107C2×D4×C43—41no—
108C2×D4×C43—41no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—416no—
112C2×D4×C43—48no—
113C2×D4×C43—48no—
114C2×D4×C43—432no—
115C2×D4×C43C2×D414yes—
116C22×C4×C43—24no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—41no—
121C22×C4×C43—44no—
122C22×C4×C43—42no—
123C22×C4×C43C22⋊C411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125M16×C43—42no—
126M16×C43—42no—
127C2×C8×C43—42no—
128C22⋊C4×C43—24no—
129C22⋊C4×C43—28no—
130C22⋊C4×C43—28no—
131C22⋊C4×C43—22no—
132C22⋊C4×C43—42no—
133C22⋊C4×C43—42no—
134C22⋊C4×C43—84no—
135C22⋊C4×C43C22⋊C414yescomplemented
136C23×C43—24no—
137C23×C43—21no—
138C23×C43—21no—
139C23×C43—216no—
140C23×C43—28no—
141C23×C43—28no—
142C23×C43—21no—
143C23×C43—24no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—44no—
153C23×C43—42no—
154C23×C43—48no—
155C23×C43—44no—
156C23×C43—42no—
157C23×C43—48no—
158C23×C43—48no—
159C23×C43—48no—
160C23×C43—416no—
161C23×C43—44no—
162C23×C43—48no—
163C23×C43—44no—
164C23×C43—48no—
165C23×C43—48no—
166C23×C43—416no—
167C23×C43—48no—
168C23×C43—44no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—48no—
172C23×C43—48no—
173C23×C43—416no—
174C23×C43—464no—
175C23×C43—416no—
176C23×C43—464no—
177C23×C43—416no—
178C23×C43—48no—
179C23×C43—48no—
180C23×C43—44no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—44no—
184C23×C43—82no—
185C23×C43—84no—
186C23×C43#9912yes—
187C23×C43#9912yes—
188C23×C43C2×C22⋊C411yescharacteristic
189C23×C43C2×C22⋊C412yes—
190C23×C43#12012yes—
191D4×C43—44no—
192D4×C43—44no—
193D4×C43—44no—
194D4×C43—416no—
195D4×C43—416no—
196D4×C43—44no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—24no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—44no—
204C2×C4×C43—48no—
205C2×C4×C43—44no—
206C2×C4×C43—82no—
207C2×C4×C43—84no—
208C2×C4×C43#12012yes—
209C8×C43—82no—
210#12687C4311yesmaximal, characteristic, direct product factor, Sylow
211C22×C43—24no—
212C22×C43—24no—
213C22×C43—22no—
214C22×C43—22no—
215C22×C43—22no—
216C22×C43—28no—
217C22×C43—22no—
218C22×C43—22no—
219C22×C43—22no—
220C22×C43—42no—
221C22×C43—42no—
222C22×C43—42no—
223C22×C43—42no—
224C22×C43—44no—
225C22×C43—432no—
226C22×C43—416no—
227C22×C43—48no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—48no—
231C22×C43—48no—
232C22×C43—416no—
233C22×C43—432no—
234C22×C43—48no—
235C22×C43—42no—
236C22×C43—42no—
237C22×C43—42no—
238C22×C43—44no—
239C22×C43—42no—
240C22×C43—41no—
241C22×C43—81no—
242C22×C43—88no—
243C22×C43—81no—
244C22×C43AΣL(1,𝔽16)14yescomplemented
245C22×C43#37911yescharacteristic
246C22×C43C2×#9911yescharacteristic
247C22×C43C2×#9911yescharacteristic
248C4×C43—22no—
249C4×C43—44no—
250C4×C43—41no—
251C4×C43—162no—
252C22×#120C2×C4311yescharacteristic
253C2×AΣL(1,𝔽16)C2×C4314yescomplemented
254#1783C2×C4311yescharacteristic, complemented
255#1781C2×C4311yescharacteristic, complemented
256C2×C43—21no—
257C2×C43—24no—
258C2×C43—21no—
259C2×C43—42no—
260C2×C43—48no—
261C2×C43—42no—
262C2×C43—42no—
263C2×C43—81no—
264C2×C43#178111yescharacteristic
265C2×C43C2×AΣL(1,𝔽16)12yes—
266C26C4×C4311yescharacteristic, complemented
267C23×D4—21no—
268C23×D4C22×C4311yescharacteristic
269C2×#120—21no—
270C2×#120—21no—
271C2×#120—28no—
272C2×#120C4×C4312yescomplemented
273C2×#120C22×C4312yes—
274C22×C22⋊C4—21no—
275C22×C22⋊C4C4×C4311yescharacteristic, complemented
276C2×#100—21no—
277C2×#100C22×C4312yescomplemented
278C2×#99—21no—
279C2×#99C22×C4312yescomplemented
280#407—21no—
281#379—21no—
282AΣL(1,𝔽16)—28no—
283C43#1268711yescharacteristic, direct product factor, Sylow
284C25—21no—
285C25—21no—
286C25—24no—
287C25—48no—
288C25—42no—
289C25—42no—
290C25C2×C4×C4311yescharacteristic
291C25C2×C4×C4312yes—
292C25D4×C4311yescharacteristic
293C22×D4—28no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—24no—
297C22×D4—42no—
298C22×D4—42no—
299C22×D4—48no—
300C22×D4C2×C4×C4311yescharacteristic
301C22×D4D4×C4311yescharacteristic
302C22×D4D4×C4311yescharacteristic
303C22×D4C23×C4311yescharacteristic
304C23×C4—21no—
305C23×C4D4×C4311yescharacteristic
306C2×M16—22no—
307#120—28no—
308#120—28no—
309#120—24no—
310#120—24no—
311#120—24no—
312#120D4×C4318yes—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4C2×C4×C4312yes—
321#100—24no—
322#100—42no—
323#99—24no—
324#99—42no—
325C22⋊C8—42no—
326C24—24no—
327C24—28no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—24no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—41no—
337C24—44no—
338C24—48no—
339C24—42no—
340C24—42no—
341C24—44no—
342C24—42no—
343C24—48no—
344C24—432no—
345C24—416no—
346C24—42no—
347C24—44no—
348C24—48no—
349C24—416no—
350C24—432no—
351C24—48no—
352C24—42no—
353C24—42no—
354C24C22⋊C4×C4311yescharacteristic
355C24C22⋊C4×C4311yescharacteristic
356C24C22⋊C4×C4311yescharacteristic
357C24C22⋊C4×C4314yescomplemented
358C24C22×C4×C4311yescharacteristic
359C24C2×D4×C4311yescharacteristic
360C2×D4—28no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—28no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—416no—
374C2×D4—48no—
375C2×D4—48no—
376C2×D4—432no—
377C2×D4C2×D4×C4314yes—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—44no—
384C22×C4—42no—
385C22×C4C22⋊C4×C4311yescharacteristic
386C22×C4C2×D4×C4311yescharacteristic
387M16—42no—
388M16—42no—
389C2×C8—42no—
390C22⋊C4—28no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—28no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—84no—
397C22⋊C4C22⋊C4×C4314yescomplemented
398C23—24no—
399C23—21no—
400C23—21no—
401C23—216no—
402C23—28no—
403C23—28no—
404C23—21no—
405C23—24no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—44no—
415C23—42no—
416C23—48no—
417C23—44no—
418C23—42no—
419C23—48no—
420C23—48no—
421C23—48no—
422C23—416no—
423C23—44no—
424C23—48no—
425C23—44no—
426C23—48no—
427C23—48no—
428C23—416no—
429C23—48no—
430C23—44no—
431C23—42no—
432C23—42no—
433C23—48no—
434C23—48no—
435C23—416no—
436C23—416no—
437C23—464no—
438C23—464no—
439C23—48no—
440C23—416no—
441C23—48no—
442C23—44no—
443C23—42no—
444C23—42no—
445C23—44no—
446C23—82no—
447C23—84no—
448C23#99×C4312yes—
449C23#99×C4312yes—
450C23C2×C22⋊C4×C4311yescharacteristic
451C23C2×C22⋊C4×C4312yes—
452C23#120×C4312yes—
453D4—44no—
454D4—44no—
455D4—44no—
456D4—416no—
457D4—416no—
458D4—44no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—82no—
469C2×C4—84no—
470C2×C4#120×C4312yes—
471C8—82no—
472C22—24no—
473C22—24no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—28no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—44no—
486C22—432no—
487C22—416no—
488C22—48no—
489C22—42no—
490C22—42no—
491C22—48no—
492C22—48no—
493C22—416no—
494C22—432no—
495C22—42no—
496C22—48no—
497C22—42no—
498C22—42no—
499C22—44no—
500C22—42no—
501C22—41no—
502C22—81no—
503C22—88no—
504C22—81no—
505C22C43×AΣL(1,𝔽16)14yescomplemented
506C22C43×#37911yescharacteristic
507C22C2×#99×C4311yescharacteristic
508C22C2×#99×C4311yescharacteristic
509C4—22no—
510C4—44no—
511C4—41no—
512C4—162no—
513C2—21no—
514C2—24no—
515C2—21no—
516C2—42no—
517C2—48no—
518C2—42no—
519C2—42no—
520C2—81no—
521C2C43×#178111yescharacteristic
522C2C2×C43×AΣL(1,𝔽16)12yes—
subgroupG/H
center, socleC22×C43C2×#99
commutatorC24C22×C4×C43
Frattini, cosocleC22×D4C23×C43
prime radicalC22×#120×C43C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C24×C43 ◁ C23×D4×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C43×AΣL(1,𝔽16)C2semidirect
3. C43×#1783C2semidirect
4. C43×#1781C2semidirect
5. C26×C43C4semidirect
11. C2×#120×C43C4semidirect
14. C22×C22⋊C4×C43C4semidirect
16. C2×#100×C43C22semidirect
18. C2×#99×C43C22semidirect
95. C24×C43C22⋊C4semidirect
135. C22⋊C4×C43C22⋊C4semidirect
210. #12687C43direct (N × H)
244. C22×C43AΣL(1,𝔽16)semidirect
253. C2×AΣL(1,𝔽16)C2×C43semidirect
254. #1783C2×C43semidirect
255. #1781C2×C43semidirect
266. C26C4×C43semidirect
272. C2×#120C4×C43semidirect
275. C22×C22⋊C4C4×C43semidirect
277. C2×#100C22×C43semidirect
279. C2×#99C22×C43semidirect
283. C43#12687direct (N × H)
357. C24C22⋊C4×C43semidirect
397. C22⋊C4C22⋊C4×C43semidirect
505. C22C43×AΣL(1,𝔽16)semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#120×C432
C2×C43×AΣL(1,𝔽16)2
C43×#17832
C43×#17812
#1268743